We exhibit a metric continuum X and a polyhedron P such that the Cartesian product X × P fails to be the product of X and P in the shape category of topological spaces.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm186-1-3, author = {J. Dydak and S. Marde\v si\'c}, title = {A counterexample concerning products in the shape category}, journal = {Fundamenta Mathematicae}, volume = {185}, year = {2005}, pages = {39-54}, zbl = {1086.54012}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm186-1-3} }
J. Dydak; S. Mardešić. A counterexample concerning products in the shape category. Fundamenta Mathematicae, Tome 185 (2005) pp. 39-54. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm186-1-3/